Question

Allegiant Airlines charges a mean base fare of $89. In addition, the airline charges for making a reservation on its website, checking bags, and inflight beverages. These additional charges average $37 per passenger. Suppose a random sample of 70 passengers is taken to determine the total cost of their flight on Allegiant Airlines. The population standard deviation of total flight cost is known to be $38. Use z-table.

a. What is the population mean cost per flight?
$

b. What is the probability the sample mean will be within $10 of the population mean cost per flight (to 4 decimals)?

c. What is the probability the sample mean will be within $5 of the population mean cost per flight (to 4 decimals)?

Answer 1

solution:-

a. the population mean cost per flight = 89 + 37 = 126

b. P(116 < x < 136)

=> P((116-126)/(38/sqrt(70)) < z < (136-126)/(38/sqrt(70)))

=> P(-2.20 < z < 2.20)

=> P(z < 2.20) - P(z < -2.20)

=> 0.9861 - 0.0139

=> 0.9722

c. P(121 < x < 131)

=> P((121-126)/(38/sqrt(70)) < z < (131-126)/(38/sqrt(70)))

=> P(-1.10 < z < 1.10)

=> P(z < 1.10) - P(z < -1.10)

=> 0.8643 - 0.1357

=> 0.7286